A crucial assumption in 2D relativistic CFT is that the EM tensor \(T(z)\)  is everywhere well-defined (finite) in the sense of correlation function [1]}. The extensive use of 2D CFT Ward identities rests on this assumption. Similarly, the finite-ness of \(\langle T^t_{\hspace{4.2679pt}t}(t,{x})X\rangle \)  whenever \(x\ne \lbrace x_p\rbrace \)  is assumed in \(1+1\) D CCFT. In particular, \(\langle T^t_{\hspace{4.2679pt}t}(t,{x})X\rangle \)  must be finite for \(x\rightarrow \infty \)  at any \(t\) . Thus the following function, holomorphic in \(x\) , is bounded:
\(H(x)\equiv \langle T^t_{\hspace{4.2679pt}t}(t,x)X\rangle +i\sum \limits _{p=1}^n\text{ }\theta (t-t_p)\left[\text{ }\sum _{k\ge 3}\text{ }\frac{{\langle Y^{(k)}_t\rangle }_p+(k-1){\langle Z_t^{(k-1)}\rangle }_p}{{(x-x_p)}^k}+\frac{{{\mathbf {\xi }_p}}\langle X\rangle }{{(x-x_p)}^2}+\frac{{\partial _{t_p}}\langle X\rangle }{x-x_p}\right]\) 
